The four documents listed below are incorporated herein by reference:    [1] Pooi Y. Kam and Hsi C. Ho, “Viterbi Detection with Simultaneous Suboptimal Maximum Likelihood Carrier Phase Estimation,” IEEE Trans. Comm., Vol. 36, No. 12, pp. 1327-1330, December 1988.    [2] O. Macchi and L. Scharf, “A Dynamic Programming Algorithm for Phase Estimation and Data Decoding on Random Phase Channels,” IEEE Trans. Inform. Theory, Vol. IT-27, No. 5, pp. 581-595, September 1981.    [3] Proakis, John G., Digital Communications, 3rd Ed., 1995, McGraw Hill, Boston, Mass.    [4] L. Hanza, T. H. Liew, and B. L. Yeap, Turbo Coding. Turbo Equalization and Space-Time Coding for Transmission over Fading Channels, IEEE Press, 2002.
In conventional digital communications receivers, a received message might consist of a preamble or acquisition sequence followed by a block of coded channel symbols that have been spread with a direct sequence spread spectrum (DSSS) code. The acquisition preamble's SNR is typically large enough to provide an estimate of the initial carrier frequency, phase, and symbol timing. The received signal typically has both symbol timing and carrier frequency drift, due to clock errors and relative motion between the receiver and transmitter.
                              y          ⁡                      (                          t              n                        )                          =                                                                              E                  s                                                  T                  s                                                      ⁢                                          c                i                            ⁡                              (                                  k                  ,                                                            t                      n                                        -                                          τ                      ⁡                                              (                                                  t                          n                                                )                                                                                            )                                      ⁢                                          m                i                            ⁡                              (                k                )                                      ⁢                          ⅇ                              j                ⁢                                                                  ⁢                                  φ                  ⁡                                      (                                          t                      n                                        )                                                                                +                      n            ⁡                          (                              t                n                            )                                                          (        1        )            A sample at time tn of a DSSS binary phase-shift keyed (BPSK) communications signal transmitted over an additive white Gaussian noise channel has the following complex form where Es denotes the constant symbol energy, ci(k,t) is the bipolar spreading function of time t for the kth data bit, i is the symbol index for the kth data bit and consist of the values {1,2} for a ½ rate code, or {1, 2, 3} for a rate 1/3 code, for example. Ts is the data symbol interval, mi(k) is the sequence of data symbols from the channel encoder output (see FIG. 1) and for BPSK modulation takes on values of ±1,τ(t) is an unknown time-varying time delay, φ(t) is an unknown time-varying carrier phase, n(t) is zero mean complex Gaussian noise with variance σn2=N0/Tad, and n is the time sample index. The received signal is sampled such thattn−tn−1=Tad  (2)where Tad is the analog-to-digital converter sample interval.
Coherent PSK communications require that the transmitter and receiver waveforms be synchronized. As mentioned above, the received signal (1) contains both an unknown timing term, τ(t), and phase term, φ(t). These unknown terms are due to transmitter and receiver clock errors and RF channel dynamics. The receiver, therefore, needs to estimate and remove these unknown time and phase terms prior to despreading and detecting the channel symbols.
The conventional coherent demodulation approach, shown in FIG. 2, is to employ phase and delay locked loops (PDLL) to track and remove unknown phase and time terms prior to channel decoding.
FIG. 3 is a block diagram for a conventional coherent data-aided Delay and Phase Locked Loop (DPLL). The input data stream, y(tn), is assumed to be a sampled complex signal defined by (1). The time tracking and phase tracking loops are implemented in parallel. The DLL consists of a pair of early and late correlators to track bit timing and despread the DSSS modulation. The data-aided PLL is implemented digitally with a Numerically Controlled Oscillator (NCO) and hard-symbol detector. The PLL performs the carrier phase tracking required to remove the unknown phase term, φ(tn). The output of the middle correlator is the complex value of the despread symbol and the phase of this term is corrected by 0 or π radians according to the sign of the detected soft symbol (i.e., a data-aided loop). The phase corrected middle correlator output is fed into the loop filters. In FIG. 3 the parameter l indicates the index of a data symbol. Dropping the subscript on mi(k) indicates the alternate indexing scheme such that m(l)=m(k+i/R) for a rate R code. This symbol index illustrates how data symbols are processed in the conventional DPLL approach.
                                          v            E                    ⁡                      (            l            )                          =                              ∑                          n              =                              l                ·                                  N                  c                                                                    n              =                                                l                  ·                                      N                    c                                                  +                                  N                  c                                -                1                                              ⁢                                                    y                ref                            ⁡                              (                                                      t                    n                                    +                                                            τ                      ^                                        ⁡                                          (                                              t                        n                                            )                                                        +                                                            δ                      ⁢                      T                                        c                                                  )                                      ⁢                          y              ⁡                              (                                  t                  n                                )                                      ⁢                          ⅇ                                                -                  j                                ⁢                                                                                                                    ⁢                    φ                                    ^                                ⁢                                  (                                      t                    n                                    )                                                                                        (        3        )            The equations for the correlators and phase detector of FIG. 3 are given as follows:
                                          v            M                    ⁡                      (            l            )                          =                              ∑                          n              =                              l                ·                                  N                  c                                                                    n              =                                                l                  ·                                      N                    c                                                  +                                  N                  c                                -                1                                              ⁢                                                    y                ref                            ⁡                              (                                                      t                    n                                    +                                                            τ                      ^                                        ⁡                                          (                                              t                        n                                            )                                                                      )                                      ⁢                          y              ⁡                              (                                  t                  n                                )                                      ⁢                          ⅇ                                                -                  j                                ⁢                                                                                                                    ⁢                    φ                                    ^                                ⁢                                  (                                      t                    n                                    )                                                                                        (        4        )                                                      v            L                    ⁡                      (            l            )                          =                              ∑                          n              =                              l                ·                                  N                  c                                                                    n              =                                                l                  ·                                      N                    c                                                  +                                  N                  c                                -                1                                              ⁢                                                    y                ref                            ⁡                              (                                                      t                    n                                    +                                                            τ                      ^                                        ⁡                                          (                                              t                        n                                            )                                                        -                                                            δ                      ⁢                      T                                        c                                                  )                                      ⁢                          y              ⁡                              (                                  t                  n                                )                                      ⁢                          ⅇ                                                -                  j                                ⁢                                                                  ⁢                                                      φ                    ^                                    ⁡                                      (                                          t                      n                                        )                                                                                                          (        5        )                                          δ          ⁢                                    φ              ^                        (            l            )                          =                  a          ⁢                                          ⁢          tan          ⁢                                          ⁢          2          ⁢                      (                                          imag                ⁢                                                                  ⁢                                  (                                                            v                      M                                        ⁡                                          (                      l                      )                                                        )                                                            real                ⁢                                                                  ⁢                                  (                                                            v                      M                                        ⁡                                          (                      l                      )                                                        )                                                      )                                              (        6        )                                          δ          ⁢                                    τ              ^                        ⁡                          (              l              )                                      =                  f          ⁡                      (                                                            v                  E                                ⁡                                  (                  l                  )                                            -                                                v                  L                                ⁡                                  (                  l                  )                                                      )                                              (        7        )            where y(tn) is the sampled input signal; yref is the reference signal used to despread the input signal, vE, vM, and vL are the integrate and dump outputs of the early, middle and late correlators, respectively; δ{circumflex over (φ)}(l) is the instantaneous phase estimate of the input signal and is obtained from the output of the middle correlator, vM, {circumflex over (φ)}(l) is the filtered phase estimate, δ{circumflex over (τ)}(l) is the instantaneous time delay estimate of the input signal and is obtained from the output of the early and late correlators, vE and vL, and {circumflex over (τ)}(l) is the filtered time delay estimate.
The performance of conventional coherent data-aided DPLLs such as described above is degraded when the symbol energy to noise power density ratio Es/No is low.
It is therefore desirable to provide for delay and phase estimation in digital communications receivers regardless of whether Es/No is low.
Exemplary embodiments of the invention provide a time delay and/or phase estimate at low Es/No by making the estimate(s) based on a convolutional decoding operation performed on the received communications signal.